Answer:
2π/3, 7π/3 and 19π/3 are the reference angles.
Explanation:
Given the angle π/3, the reference angle to this angle is the angle similar to the given angle.
The angle similar to the angle is derived by adding 2πk to each resulting angle where k is integers from 1 and above
Given initial angle of π/3
The following are the reference angles:
When k = 1
theta(k) = π/3 + 2πk
theta(1) = π/3 + 2π(1)
=(π+6π)/3
= 7π/3
When k = 2
theta(2) = π/3 + 2π(2)
= π/3 + 4π
=(π+12π)/3
= 13π/3
When k = 3
theta(2) = π/3 + 2π(3)
= π/3 + 6π
=(π+18π)/3
= 19π/3
Note that π-theta is also a reference angle where theta us the given angle.
π-theta= π-π/3
= 3π-π/3
= 2π/3
From the calculation above, 2π/3, 7π/3 and 19π/3 are the reference angles.